An optical resonance occurs when light waves confined by total internal reflection in a closed loop dielectric microstructure are reflected back on the same optical path where they build up in intensity over multiple round-trips due to constructive interference. For materials with a constant refractive index, in order for light to interfere constructively inside the resonator, the optical path length must be an integer multiple of the wavelength of the light and therefore the resonant conditions can occur only at certain wavelengths. (See, e.g.: Bahaa Saleh, Malvin Teich, “Fundamentals of Photonics,” (New York: Wiley, 1991) (incorporated herein by reference); John Jackson, “Classical Electrodynamics,” (New York etc.: Wiley, 1962) (incorporated herein by reference); Andrey B. Matsko, and Vladimir S. Ilchenko, “Optical Resonators with Whispering—Gallery Modes—Part I: Basics,” IEEE Journal Selected Topics in Quantum Electronics, 12(1) 3-14, (2006) (incorporated herein by reference); and David K. Cheng, “Field and Wave Electromagnetics,” (New York: Addison-Wesley, 1989) (incorporated herein by reference).) A shift in optical resonance frequency due to change in surrounding conditions has been used for different types of measurements and detections. (See, e.g.: Vladimir S. Ilchenko, and Andrey B. Matsko, “Optical Resonators with Whispering-Gallery Modes—Part II: Applications,” IEEE Journal of Selected Topics in Quantum Electronics, 12(1), pp. 15-32, (2006) (incorporated herein by reference); F. Vollmer, et al., “Protein Detection by Optical Shift of a Resonant Microcavity,” Applied Physics Letters 80.21 (2002): 4057-4059 (incorporated herein by reference); and Anisur Rahman, and Sunil Kumar, “Optical Resonance in Dielectric Micro-sphere for Temperature Measurement.” ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference collocated with the ASME 2007 InterPACK Conference, American Society of Mechanical Engineers, 2007 (incorporated herein by reference).) Microstructures that generate optical resonances and exploit their properties for various applications have primarily been confined to the geometric shapes of sphere, cylinder, disk, or circular rings.
In the last decade, circular microring, solid sphere, and solid disk optical dielectric microresonators have been studied intensively due to potential applications, primarily in optical communications, biomedical sensing, spectroscopy, micro or nano-level measurements and detection, quantum mechanics, etc. The solid sphere and disk microresonators are multimode since more than one resonant mode is present. (See, e.g.: Vollmer, F., et al. “Protein Detection by Optical Shift of a Resonant Microcavity,” Applied Physics Letters, 80.21 (2002): 4057-4059 (incorporated herein by reference); Rahman, Anisur, and Sunil Kumar, “Optical Resonance in Dielectric Micro-Sphere for Temperature Measurement.” ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference collocated with the ASME 2007 InterPACK Conference, American Society of Mechanical Engineers, 2007 (incorporated herein by reference); A. Rahman, R. Eze, and S. Kumar, “Novel Optical Sensor Based on Morphology-Dependent Resonances for Measuring Thermal Deformation in Microelectromechanical Systems Devices,” Journal of Micro/Nanolithography, MEMS, and MOEMS 8.3 (2009): 033071-033071 (incorporated herein by reference); Keng, Ta Kang David, Whispering Gallery Mode Bioparticle Sensing and Transport, Doctoral Dissertation, Polytechnic Institute of New York University, 2009 (incorporated herein by reference); Kerry Vahala, “Optical Microcavities”, Nature, 424(6950), pp. 839-846, 2003 (incorporated herein by reference); Wladyslaw Zakowicz, “Whispering-Gallery-Mode Resonances: A New Way to Accelerate Charged Particles”, Physical Review Letters, 95, pp. 114801-1-114801-4, 2005 (incorporated herein by reference).) Challenges for evanescent coupling of circular, ring, disk, cylindrical, and spherical microresonators are due to the short interaction length and a tight submicrometer gap required between the curved resonator sidewall of the microresonator and the straight waveguide(s) coupling light from a source to the microresonator, and from the microresonator to a detector (See, e.g.: Guo, Z., Quan, H., & Pau, S, “Gap effects on whispering-gallery mode microresonances,” Optics East, International Society for Optics and Photonics, (2005): 600204-600204 (incorporated herein by reference); Bogaerts, W., De Heyn, P., Van Vaerenbergh, T., De Vos, K., Kumar Selvaraja, S., et al., “Silicon microring resonators,” Laser & Photonics Reviews, 6.1, (2012): 47-73 (incorporated herein by reference); and Yan, S., Li, M., Luo, L., Ma, K., Xue, C., and Zhang, W, “Optimisation Design of Coupling Region Based on SOI Micro-Ring Resonator,” Micromachines, 6.1, (2014): 151-159 (incorporated herein by reference).)
Recently, solid dielectric multimode square-shaped microresonators have attracted interest as they offer (1) longer evanescent coupling lengths, and (2) a relatively simple geometry for fabrication. (See, e.g.: Poon, A. W., F. Courvoisier, and R. K. Chang, “Multimode Resonances in Square-Shaped Optical Microcavities,” Optics Letters, 26.9 (2001): 632-634 (incorporated herein by reference); Boriskina, Svetlana V., et al. “Optical Modes in 2-D Imperfect Square and Triangular Microcavities,” Quantum Electronics, IEEE Journal of, 41.6 (2005): 857-862 (incorporated herein by reference); Guo, Wei-Hua, et al. “Modes in Square Resonators,” Quantum Electronics, IEEE Journal of, 39.12 (2003): 1563-1566 (incorporated herein by reference); Guo, Wei-Hua, et al. “Whispering-Gallery-Like Modes in Square Resonators,” Quantum Electronics, IEEE Journal of, 39.9 (2003): 1106-1110 (incorporated herein by reference); Moon, Hee-Jong, et al. “Whispering Gallery Mode Lasing in a Gain-Coated Square Microcavity with Round Corners,” Japanese Journal of Applied Physics 42.6B (2003): L652 (incorporated herein by reference); Fong, Chung Yan, and Andrew Poon. “Mode Field Patterns and Preferential Mode Coupling in Planar Waveguide-Coupled Square Microcavities,” Optics Express 11.22 (2003): 2897-2904 (incorporated herein by reference); and Abdul Latiff, Anas, et al., “Design High-Q Square Resonator Add-Drop Filter for CWDM Application,” Australian Journal of Basic and Applied Sciences 7.10 (2013): 364-367 (incorporated herein by reference).) Unfortunately, however, the quality factor (“Q-factor”), which is an indicator of energy loss (high Q-factor implies low energy loss), of such solid square resonators is very small and can be negatively impacted due to optical losses at sharp-corners of such microresonators. Furthermore, multimode resonators typically do not provide the desired accuracy for nano-scale or micro-scale detection, in which resonance shifts on the order of a picometer may need to be detected. Additionally, optical resonances in square structures are not prominent and not distinguished by the sharp peaks that typically characterize high quality resonances. (See, e.g., Li, Chao, and Andrew W. Poon, “Experimental Demonstration of Waveguide-Coupled Round-Cornered Octagonal Microresonators in Silicon Nitride,” Optics Letters 30.5 (2005): 546-548 (incorporated herein by reference).)
Therefore, it would be useful to simultaneously solve the problems of difficult fabrication and evanescent coupling found in circular microresonators, and low Q-factor found in square or other sharp-cornered microresonators.